x(x+5)=2(x+3)

Solution for x(x+5)=2(x+3) equation:

x(x+5)=2(x+3)

We move all terms to the left:

x(x+5)-(2(x+3))=0

We multiply parentheses

x^2+5x-(2(x+3))=0


We calculate terms in parentheses: -(2(x+3)), so:

2(x+3)

We multiply parentheses

2x+6

Back to the equation:

-(2x+6)


We get rid of parentheses

x^2+5x-2x-6=0

We add all the numbers together, and all the variables

x^2+3x-6=0

a = 1; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·1·(-6)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{33}}{2*1}=\frac{-3-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*1}=\frac{-3+\sqrt{33}}{2}
$